Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#33903 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| prime radical | C2×D4×C59 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C4×D4×C59 ◁ C8×D4×C59 ◁ G | |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,5,4)(3,7,8,6)(9,10)(11,15)(12,16)(13,26)(14,19)(17,23)(18,24)(20,27)(21,36)(22,30)(25,32)(28,33)(29,34)(31,37)(35,39)(38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3)(2,6)(4,7)(5,8)(9,11,14,22)(10,15,19,30)(12,20,25,35)(13,21,24,34)(16,27,32,39)(17,28,31,38)(18,29,26,36)(23,33,37,40);(1,4,5,2)(3,7,8,6)(10,16)(12,23)(13,24)(15,27)(17,18)(19,32)(20,33)(21,34)(25,37)(26,31)(28,29)(30,39)(35,40)(36,38);(3,8)(6,7)3245 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26891);